Efficiency at maximum power of Feynman's ratchet as a heat engine

Abstract

The maximum power of Feynman's ratchet as a heat engine and the corresponding efficiency (${\eta }_{\ast }$) are investigated by optimizing both the internal parameter and the external load. When a perfect ratchet device (no heat exchange between the ratchet and the paw via kinetic energy) works between two thermal baths at temperatures $T_1>T_2$, its efficiency at maximum power is found to be ${\eta }_{\ast }={\eta }_C^2/[{\eta }_C-(1-{\eta }_C)\ln (1-{\eta }_C)]$, where ${\eta }_C\equiv 1-T_2/T_1$. This efficiency is slightly higher than the value $1-\sqrt{T_2/T_1}$ obtained by Curzon and Ahlborn [\textit{Am. J. Phys.} \textbf{43} (1975) 22] for macroscopic heat engines. It is also slightly larger than the result ${\eta }_{SS}\equiv 2{\eta }_C/(4-{\eta }_C)$ obtained by Schmiedl and Seifert [\textit{EPL} \textbf{81} (2008) 20003] for stochastic heat engines working at small temperature difference, while the evident deviation between ${\eta }_{\ast }$ and ${\eta }_{SS}$ appears at large temperature difference. For an imperfect ratchet device in which the heat exchange between the ratchet and the paw via kinetic energy is non-vanishing, the efficiency at maximum power decreases with increasing the heat conductivity.

7 pages, 3 figures; correct some errors

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